Search results

Items from 1 to 20 out of 45 results

article

The Henstock‐Kurzweil‐Pettis integral and multiorders fractional differential equations with impulses and multipoint fractional integral boundary conditions in Banach spaces

Djamila Seba, Sadek Habani, Abbes Benaissa, Hamza Rebai

Mathematical Methods in the Applied Sciences > 44 > 10 > 8345 - 8362

This paper is devoted to the existence of weak solutions for a multipoint fractional integral boundary value problem of an impulsive nonlinear differential equation involving multiorders fractional derivatives and deviating argument. We make use of an appropriate fixed point theorem combined with the technique of measures of weak noncompactness. Our investigation is considered in a Banach space. The...

article

Existence results for a class of nonlinear singular transport equations in bounded spatial domains

Khalid Latrach, Hssaine Oummi, Ahmed Zeghal

Mathematical Methods in the Applied Sciences > 43 > 4 > 1685 - 1700

In this paper, we prove the existence of solutions to a nonlinear singular transport equation (ie, transport equation with unbounded collision frequency and unbounded collision operator) with vacuum boundary conditions in bounded spatial domain on L^p‐spaces with 1 ≤ p<+∞. This problem was already considered in^6,8,9 under the hypothesis that the collision frequency σ(·) and the collision operator...

article

Fixed point theorems for monotone mappings in ordered Banach spaces under weak topology features

Abdullah Alahmari, Mohamed Mabrouk, Mohamed-Aziz Taoudi

Journal of Mathematics and Applications > 2019 > Vol. 42 > 5--19

We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vectorvalued ordinary differential equations. Our conclusions generalize many well-known results.

article

Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces

Afif Ben Amar, Saoussen Derbel, Donal O’Regan, Tian Xiang

Journal of Fixed Point Theory and Applications > 2019 > 21 > 1 > 1-25

In this paper, we establish new fixed point results for some weakly countably condensing and weakly sequentially continuous maps, fixed-point results of Krasnosel’skii–Daher type for the sum of two weakly sequentially continuous mappings in Banach spaces, a multivalued version of the Daher fixed point theorem for weakly countably condensing multimaps having w-weakly closed graph in Banach spaces and...

article

Existence of weak solutions for a boundary value problem of a second order ordinary differential equation

Shiyou Weng, Fuli Wang

Boundary Value Problems > 2018 > 2018 > 1 > 1-11

The aim of this paper is to investigate the existence of weak solutions for a boundary value problem of a second order differential equation. As the main tool, we apply a Krasnosel’skii type fixed point theorem in conjunction with the technique of measures of weak noncompactness in Banach spaces. Finally, two examples are given to illustrate our abstract results.

article

Weak solutions for a coupled system of Pettis-Hadamard fractional differential equations

Saïda Abbas, Mouffak Benchohra, Yong Zhou, Ahmed Alsaedi

Advances in Difference Equations > 2017 > 2017 > 1 > 1-11

In this paper, by applying the technique of measure of weak noncompactness and Mönch’s fixed point theorem, we investigate the existence of weak solutions under the Pettis integrability assumption for a coupled system of Hadamard fractional differential equations.

article

A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

Saïd Abbas, Mouffak Benchohra, Jamal-Eddine Lazreg, Yong Zhou

Chaos, Solitons & Fractals > 2017 > 102 > C > 47-71

In the present survey paper, we prove some results concerning the existence of solutions and weak solutions for some classes of Hadamard and Hilfer fractional differential equations. Some attractivity and Ulam stability results are presented. Our results are provided by applying the fixed point theory, and the technique of strong and weak measures of noncompactness.

article

Heterogeneous Vectorial Fixed Point Theorems

Tiziana Cardinali, Radu Precup, Paola Rubbioni

Mediterranean Journal of Mathematics > 2017 > 14 > 2 > 1-12

In this paper, we obtain fixed point theorems for operators defined on Cartesian product spaces under heterogeneous conditions upon the structure of the factor spaces and the operator components. The main results combine Banach–Perov contraction principle with topological fixed point theorems of Mönch type in strong and weak topologies. The results make possible a tinted analysis of the operator systems...

article

Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces

Baolin Li, Haide Gou

Boundary Value Problems > 2016 > 2016 > 1 > 1-13

The aim of this paper is to discuss the existence of weak solutions for a nonlinear two-point boundary value problem of integrodifferential equations of fractional order α ∈ ( 1 , 2 ] $\alpha\in(1,2]$ . Our analysis relies on the Krasnoselskii fixed point theorem combined with the technique of measure of weak noncompactness.

article

Fixed point theorems for the sum of (ws)-compact and asymptotically $${\Phi}$$ Φ -nonexpansive mappings

Afif Ben Amar, Donal O’Regan, Amel Touati

Journal of Fixed Point Theory and Applications > 2016 > 18 > 4 > 771-784

In this paper, we introduce the concept of an asymptotically $${\Phi}$$ Φ -nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically $${\Phi}$$ Φ -nonexpansive operator on an unbounded closed convex subset of a Banach...

article

On the solutions for a nonlinear boundary value problem modeling a proliferating cell population with inherited cycle length

Abdul-Majeed Al-Izeri, Khalid Latrach

Nonlinear Analysis: Theory, Methods & Applications > 2016 > 143 > C > 1-18

This paper deals with existence results for a nonlinear boundary value problem derived from a model introduced by Lebowitz and Rubinow (1974) describing a proliferating cell population. Cells are distinguished by age a and cycle length l. The cycle length is viewed as an inherited property determined at birth. The boundary condition models the process of cell division of mother cells and the inheritance...

article

Integrable solutions of a generalized mixed-type functional integral equation

Haydar Abdel Hamid, Waad Al Sayed

Applied Mathematics and Computation > 2016 > 276 > C > 356-366

In this work, we prove the existence of integrable solutions for the following generalized mixed-type nonlinear functional integral equation x(t)=g(t,(Tx)(t))+f(t,∫0tk(t,s)u(t,s,(Qx)(s))ds),t∈[0,∞). Our result is established by means of a Krasnosel’skii type fixed point theorem proved by Taoudi (2009). In the last section we give an example to illustrate our result.

article

Existence Results for a Nonlinear Transport Equation with Unbounded Admissible Velocities Space

M. Boumhamdi, K. Latrach, A. Zeghal

Mediterranean Journal of Mathematics > 2016 > 13 > 5 > 3155-3171

In this paper, we discuss existence results for the nonlinear boundary value problem (1.1)–(1.2) on $${L^{1}}$$ L 1 -spaces. This problem was already considered in Latrach and Zeghal (J Appl Math Comp 219:1163–1172, 2012) under the hypothesis that the velocity space has finite measure. This condition was used to establish a compactness result necessary to use fixed point theorems. In this...

article

Fixed point theorems for multivalued mappings in ordered Banach spaces with application to integral inclusions

Nawab Hussain, Mohamed-Aziz Taoudi

Fixed Point Theory and Applications > 2016 > 2016 > 1 > 1-9

This paper provides new common fixed point theorems for pairs of multivalued and single-valued mappings operating between ordered Banach spaces. Our results lead to new existence theorems for a system of integral inclusions.

article

Leray-Schauder-type fixed point theorems in Banach algebras and application to quadratic integral equations

Abdelmjid Khchine, Lahcen Maniar, Mohamed-Aziz Taoudi

Fixed Point Theory and Applications > 2016 > 2016 > 1 > 1-20

In this paper, we present new fixed point theorems in Banach algebras relative to the weak topology. Our fixed point results are obtained under Leray-Schauder-type boundary conditions. These results improve and complement a number of earlier works. As an application, we establish some existence results for a broad class of quadratic integral equations.

article

On the Solvability of a Nonlinear Integro-Differential Equation on the Half-Axis

Azzeddine Bellour, Mahmoud Bousselsal, Mohamed-Aziz Taoudi

Mediterranean Journal of Mathematics > 2016 > 13 > 5 > 2887-2896

In this work, we combine the iterative techniques with fixed point theory to investigate the existence of absolutely continuous solutions to a class of nonlinear integro-differential equations. Existence results are obtained under fairly simple conditions of Carathéodory type.

article

On the Existence of Weak Solutions of Nonlinear Integral Equations in Banach Spaces

Baolin Li, Haide Gou

Mediterranean Journal of Mathematics > 2016 > 13 > 5 > 2633-2643

In this paper, we use the techniques of measure of weak noncompactness and Henstock–Kurzweil–Pettis integrals to discuss the existence theorem of weak solutions for a class of the nonlinear integral equations and obtain a new result, which improves and extends some relevant results for differential and integral equations in Banach spaces.

article

Existence results for a nonlinear version of Rotenberg model with infinite maturation velocities

Mounir Boumhamdi, Khalid Latrach, Ahmed Zeghal

Mathematical Methods in the Applied Sciences > 38 > 9 > 1795 - 1807

In this paper, we present some existence results on L¹ spaces of a nonlinear boundary value problem derived from a model introduced by Rotenberg (1983) describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturity μ ∈ [0,1] and its maturation velocity v. The biological boundary at μ = 0 and μ = 1 are fixed and tightly coupled through the mitosis...

article

Radon–Nikodým indexes and measures of weak noncompactness

B. Cascales, A. Pérez, M. Raja

Journal of Functional Analysis > 2014 > 267 > 10 > 3830-3858

The aim of this paper is to present a quantitative version of the Radon–Nikodým property and some other results related to it. This approach gives an extra insight to the classical results. We introduce two indexes: an index of representability of measures and an index of dentability. We review classic results in order to obtain relationships between these and other indexes.

article

The Leray-Schauder condition for 1-set weakly-contractive and (ws)-compact operators

Afif BEN AMAR

Acta Mathematica Scientia > 2014 > 34 > 2 > 263-273

The main purpose of this article is to prove a collection of new fixed point theorems for (ws)-compact and so-called 1-set weakly contractive operators under Leray-Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for (ws)-compact...

Publication date

Set your own date range

INFONA - science communication portal

Search results

The Henstock‐Kurzweil‐Pettis integral and multiorders fractional differential equations with impulses and multipoint fractional integral boundary conditions in Banach spaces

Existence results for a class of nonlinear singular transport equations in bounded spatial domains

Fixed point theorems for monotone mappings in ordered Banach spaces under weak topology features

Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces

Existence of weak solutions for a boundary value problem of a second order ordinary differential equation

Weak solutions for a coupled system of Pettis-Hadamard fractional differential equations

A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

Heterogeneous Vectorial Fixed Point Theorems

Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces

Fixed point theorems for the sum of (ws)-compact and asymptotically $${\Phi}$$ Φ -nonexpansive mappings

On the solutions for a nonlinear boundary value problem modeling a proliferating cell population with inherited cycle length

Integrable solutions of a generalized mixed-type functional integral equation

Existence Results for a Nonlinear Transport Equation with Unbounded Admissible Velocities Space

Fixed point theorems for multivalued mappings in ordered Banach spaces with application to integral inclusions

Leray-Schauder-type fixed point theorems in Banach algebras and application to quadratic integral equations

On the Solvability of a Nonlinear Integro-Differential Equation on the Half-Axis

On the Existence of Weak Solutions of Nonlinear Integral Equations in Banach Spaces

Existence results for a nonlinear version of Rotenberg model with infinite maturation velocities

Radon–Nikodým indexes and measures of weak noncompactness

The Leray-Schauder condition for 1-set weakly-contractive and (ws)-compact operators

Filter options

Publication date

Content availability

Keywords

Data set

INFONA - science communication portal

Search results

Add recipient

Sending message cancelled

Are you sure you want to cancel sending this message?

Send message

Filter options

Publication date

Date range setting

Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.

Content availability

Keywords

Data set

Reporting an error / abuse

Sending the report failed

Accessibility options